Scoring functions are commonly used to evaluate a point forecast of a particular statistical functional. This scoring function should be consistent, meaning the correct value of the functional is the Bayes act, in which case we say the scoring function elicits the functional. Recent results show that the mode functional is not elicitable. In this work, we ask whether it is at least possible to indirectly elicit the mode, wherein one elicits a low-dimensional functional from which the mode can be computed. We show that this cannot be done: Neither the mode nor a modal interval is indirectly elicitable with respect to the class of identifiable functionals.

中文翻译：

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关于模态和模态区间的间接引出性

评分函数通常用于评估特定统计函数的点预测。这个评分函数应该是一致的，这意味着函数的正确值是贝叶斯行为，在这种情况下，我们说评分函数引出函数。最近的结果表明模式泛函是不可引出的。在这项工作中，我们询问是否至少可以间接引出模式，其中可以引出一个低维函数，从中可以计算出模式。我们证明这是不可能的：对于可识别的泛函类，模式和模态区间都不能间接引出。